Solve the electric field strength of the capacitor's dielectric when the polarization P=2μCm2P=2μCm2, the relative permittivity of the dielectric is εr=5.5εr=5.5 and when the permittivity of the vacuum is known ε0=8.854∗10−12Fm



To solve for the electric field strength \( E \) in the dielectric of a capacitor, given the polarization \( P = 2 \, \mu C/m^2 \), relative permittivity \( \varepsilon_r = 5.5 \), and permittivity of vacuum \( \varepsilon_0 = 8.854 \times 10^{-12} \, F/m \), we can use the following relation:

\[
P = \varepsilon_0 (\varepsilon_r - 1) E
\]

Where:
- \( P \) is the polarization,
- \( \varepsilon_0 \) is the vacuum permittivity,
- \( \varepsilon_r \) is the relative permittivity of the dielectric, and
- \( E \) is the electric field strength.

We want to solve for \( E \):

\[
E = \frac{P}{\varepsilon_0 (\varepsilon_r - 1)}
\]

Now, let's plug in the values:
- \( P = 2 \times 10^{-6} \, C/m^2 \)
- \( \varepsilon_0 = 8.854 \times 10^{-12} \, F/m \)
- \( \varepsilon_r = 5.5 \)

\[
E = \frac{2 \times 10^{-6}}{8.854 \times 10^{-12} \times (5.5 - 1)}
\]

\[
E = \frac{2 \times 10^{-6}}{8.854 \times 10^{-12} \times 4.5}
\]

Now let's calculate \( E \).The electric field strength \( E \) in the dielectric is approximately \( 50,197 \, \text{V/m} \).

Would you like more details or have any questions about this solution?

Here are five related questions for further exploration:
1. How does the electric field strength change with varying polarization \( P \)?
2. What effect does increasing the relative permittivity \( \varepsilon_r \) have on the electric field strength?
3. How does the electric field strength compare in a vacuum versus in a dielectric?
4. Can you calculate the electric field strength if the relative permittivity is doubled?
5. What is the relationship between capacitance and the electric field in a dielectric material?

**Tip:** The electric field inside a dielectric material is always weaker than in a vacuum, due to the dielectric's ability to polarize and reduce the field strength.

Solve the electric field strength of the capacitor's dielectric when the polarization P=2μC/m², the relative permittivity of the dielectric is εr=5.5, and the permittivity of the vacuum is known ε0=8.854×10⁻¹² F/m.

This page explains how to solve for the electric field strength in a capacitor's dielectric given polarization P=2μC/m², relative permittivity εr=5.5, and vacuum permittivity ε0=8.854×10⁻¹² F/m. A detailed step-by-step solution using the formula E = P / [ε₀(εr - 1)] is provided. Suitable for college-level physics students.

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